Are Six 100 Year Storms Across the GTA Rare Over a 14 Year Period When Considering Probabilities of Observing Extremes at over 150 Rain Gauges?

Roll a 100-sided die once. That is what looking
for a 100 Year storm at a single rain gauge
in a single year is like.
A motion at the City of Toronto notes the following regarding extreme rainfall in the GTA: "According to the Insurance Bureau of Canada, the Greater Toronto Area has had six “100 Year Storms” since 2005". See Mike Layton motion here:

CBC has reported on this: link

While we are all concerned about flooding, the question on large storm frequency is "So What?". Or more specifically, from a statistical, mathematical, logical point of view, is more than five 100 Year storms over a 14 year period (2005 to 2018) rare and unexpected, or does this have a high probability of occurring? As we know the Insurance Bureau of Canada does not always rely on proper statistics to support statements on extreme weather, confusing theoretical shifts in probabilities of extreme events with real data (see IBC Telling the Weather Story where IBC ignores Environment and Climate Change Canada's Engineering Climate Datasets).

Let's do some math to see if over five 100 Year storms is rare or not.

First, consider that a 100 Year storm has a probability of occurring of 1/100 = 1 percent per year.


Second, count up the number of rain gauges that have been proliferating across the GTA to support inflow in infiltration studies for wastewater studies and to support operational needs. Here are some counts with various sources:

i) City of Toronto ( - 46 rain gauges

ii) Region of York ( - 71 rain gauges

iii) Peel Region ( - 6 rain gauges (correction July 25, 2019 - Peel has 28 rain gauges ... probabilities in this blog post will go up a bit)

iv) Halton Region ( - 14 rain gauges

v) Toronto and Region Conservation Authority ( - 14 rain gauges

Total number of gauges = 151. A good first estimate - certainly there are more. (correction July 25, 2019 - as Peel has 28 rain gauges the total is 173 stations)


Third, assuming each rain gauge observes rainfall events independently year to year, what is the chance of getting at least one 100 Year event at a single gauge in 14 years?

Probability = 1 - (1-1/100)^14 = 13.1% chance of a 100 Year storm storm at a single gauge. That seems pretty big.

The number of 'trials' or samples equivalent to 14 rolls of a 100-sided die, meaning 14 independent observations or 'samples' from the statistical population of events.

It is reasonable to assume that a single rain gauge can record a 100 Year event but not surrounding gauges? Yes indeed. The August 2018 storm in Toronto only exceeded 100 Year rainfall totals at one gauge. So it is reasonable for smaller, spatially isolated rainfall events that do occur.


Fourth, assuming all rain gauges observe rain independently what is the chance of getting more than one 100 Year events across all 151 gauge in 14 years?

The number of trials/samples/observations = 151  x 14 = 2114

Probability = 1 - (1-1/100)^(2114) = over 99.9% chance of at least one 100 year storm at 151 independent gauges. That is almost a certainty.

(Additional comment: we know that storms exceeding 100 Year volumes can cover large areas such that observations are adjacent gauges are not completely independent, especially if they are spatially very close - so this fourth scenario is considered an upper bound on sensitivity analysis considering gauge independence - below, another bound is evaluated assuming less independence).

What about more than five 100 Year storms over 14 years? We have to then consider combinations of events (we do not care which of the 2144 samples has the events) and approach this by subtracting the probability of 1, 2, 3, and 4 events. This summarizes the approach (thanks so much FP!):

The probability of 5 or more 100 Year events is again over 99.9% (see cell F22), showing that when there are many, many trials, the probability of a multiple rare event is very high.


Fifth, assuming large storms cluster across several gauges and they do not operate independently from each other for extreme events, and that say they observe 100 Year storms in groups of 5, what is the chance of getting one 100 Year event across 151/5 = 30.2 rain gauge clusters in 14 years?

The number of trials/samples/observations = (151 x 14) / 5 = 2114 / 5 = 422.8

Probability = 1 - (1-1/100)^(422.8) = over 98.5% chance of at least one 100 year storm at 30 independent gauge clusters.  Near certainty. Not rare at all!

Let's consider over five 100 Year storms again. A keen reader has shown that the probability is 41.6% for this, as shown in cell L22 in the spreadsheet image above. Again,pretty high chance of getting 5 or more events when gauges do not observe extremes independently, but rather in clusters.

For more on this analysis, and the probability of 5 or more occurrences in 423 observations the probabilities considered in deriving the probability are as follows:
  • 4 occurrences in 423 observations (P = 0.195038119)
  • 3 occurrences in 423 observations (P = 0.183893083)
  • 2 occurrences in 423 observations (P = 0.1297298)
  • 1 occurrences in 423 observations (P = 0.060868484)
  • 0 occurrences in 423 observations (P = 0.014245815)
  • Sum = 0.583775302
So P[ X ≥ 5; 423] = 1 - 0.583775302 = 0.416224698, or 41.6% noted above. This is the common approach for deriving the probability of a scenario, i.e., by subtracting the probability of the event not occurring from 1.0 (the probability of all events). In this case the sum of the probability of zero to 4 observations occurring is the probability of the scenario of interest (5 occurrences or more) not occurring. If you are interested in testing other scenarios and assumptions for size of rain gauge clusters, use this helpful web site (also used to check the calculations in the spreadsheet shared above): Below are checks of the probability analysis:

Probability of 5 or more 100 Year Storms at Independent Rain Gauges (151 gauges x 14 years = 2114 'trials')
Probability of 5 or more 100 Year Storms at Clusters of Rain Gauges With Dependent  Observations (30.2 gauge clusters x 14 years = 422.8, say 423, 'trials')
There are more rain gauges in Durham Region and other Conservation Authorities in the GTA which means there may be more than 30 clusters to observe extreme weather in, meaning an even higher probability of observing extreme events.

So about 423 rolls of a 100-sided die may result in more than five occurrences of a single number with a relatively high probability. If the clusters are bigger, the probability is a bit less, but as we have seen, sometimes only one gauge 'sees' the 100 Year extreme rain. If gauges observe events in clusters of 10, which is an extreme end of the range as we have examples of storms affecting only one gauge (August 2018 in Toronto), there is still a probability for 5 events of over 5% (see below):

Probability of 5 or more 100 Year Storms at Large Clusters of Rain Gauges With Dependent  Observations (15.1 gauge clusters x 14 years = 211.4, say 211, 'trials')
Past flood events in Toronto reveal that between 1 and 13 rain gauges observe 100 Year rainfall depth, as shown in this Toronto Water presentation:
It shows:

  • May 12, 2000 - 1 rain gauge over 100 Year (see slide 9)
  • August 19, 2005 - 12 rain gauges over 100 Year (see slide 11)
  • July 13, 2018 - 6 rain gauges over 100 Year (see slide 19)
The August 7, 2018 flood in Toronto was due to only one Toronto rain gauge in the Open Data dataset exceeding 100 Year volumes. Therefore, assuming a cluster size of 5 dependent rain gauges within independent clusters that observe extreme events seems quite reasonable.

Conclusion - is it not rare to get more than five 100 Year rainfall observations at over 151 GTA gauges, over 14 years. The chances range from near certainty (over 99.9%) for independent events at each rain gauge to relatively high probability (over 40%) if gauges are independent clusters of 5 or more.


So what else does that tell us? There is a tendency to exercise an 'availability bias' in the words of Daniel Kahneman, and ignore statistics when making quick observations about extreme events. A description of this and other "Thinking Fast" heuristic biases surrounding flooding and extreme weather is in this paper.

Most media reports seldom "do math" and echo sources without question many times - that was the finding of the CBC Ombudsman on this topic of more frequent or severe extreme rainfall recently - see Ombudsman ruling.

Its one thing for a reporter to echo IBC statements on extreme weather for a news story, but Toronto should be careful in taking on a court case with limited data - it would be great to see any IBC statistics or analysis (unlike in the Telling the Weather Story communications). Toronto should also be aware that its flood problems are due mainly to its own design standards in the original size municipalities dating back before the 1980's. Spatial analysis shows that is where the risks are and where the flood reports are being made to the City of Toronto - see slide 36 in this review of flood risk factors which clearly do not include more extreme weather - partially separated systems have the highest risk and Toronto has allowed development to occur without mitigating risks in the past (hence the famous Scarborough Golf court case decision against municipalities for gaps in their stormwater management practices (Scarborough Golf Country Club Ltd v City of Scarborough et al)). Same thing on other GTA cities - see slide 7 in this presentation to the National Research Council's national workshop on urban flooding February 2018 for flood vulnerabilities in the City of Markham - see where Mississauga flood calls occur in this previous post (more than half of flood calls are in pre-1980 areas designed with limited resiliency for extreme weather).

So there has always been flooding:

And the most extreme rainfall intensities in Toronto over short durations happened in the 1960's:

And now extreme rainfall statistics from Environment and Climate Change Canada show decreasing short duration intensities since 1990 in and around Toronto:

.. as shown in a previous post. These 5 minute 100 Year intensities have dropped between 4.0 % and 8.1% between 1990 and 2016-2017 depending on the location.

Such decreases in short duration intensities are happening across southern Ontario as well, based on the newest Engineering Climate Datasets as shown here. Toronto should be careful in preparing for a legal challenge and any claims on flood causes.

As noted in my recent Financial Post OpEd, making a big deal about irrelevant risk facts distracts us from addressing the root cause of flood problems. The City of Toronto should try to not get distracted. And Councilor Mike Layton is probably in the running for a Milli Vanilli "Blame it on the Rain" award this year :)


Terence Corcoran covers this all very well in today's column, referencing analysis on this blog.

Note: probabilities for 5 or more events corrected/updated April 1, 2019. Thanks to keen readers for helping define the probabilities of combination events and for the nostalgic references to University of Toronto's Professor Emeritus Dr. Barry Adams' CIV340 course notes that outline the analysis approach.


What are the probabilities considering the updated number of stations (i.e., more in Peel), meaning a total of 173 stations? That is, 2422 trials if stations are independent and 484 trials if stations are clustered in clusters of 5.

For 5 or more 100-year storms in 14 years, the probability is 99.9% - 53.2% for independent and clustered gauges, respectively.

For 6 or more storms the probability is 99.9% - 35.6% for independent and clustered gauges, respectively.

Disaster Mitigation Adaptation Fund - Infrastructure Canada Announces Toronto, Vaughan , Markham, Regional Municipality of York Grants

Disaster Mitigation Adaptation Fund (DMAF) funding has been announced for Alberta and Ontario - the announcement for GTA municipalities has been made March 26.  Funding in the City of Toronto, City of Vaughan and the City of Markham is focused on earlier development areas with limited design standards for municipal infrastructure and limited land use planning surrounding floodplain hazard management. The total funding is $150,388,000.

The Markham projects fall under its long term Flood Control Program and include sewer upgrades in the West Thornhill community where Phase 3 and Phase 4 are being 40% funded through DMAF, the Don Mills Channel flood control upgrades including a central wetland storage/floodplain restoration will replace vulnerable properties to be purchased as well as culvert upgrades, and sewer upgrades in the vicinity of the Thornhill Community Centre which will reduce flood risks for vulnerable populations. Details on the West Thornhill Project are here: link, and the Don Mills Channel project details are here: link

The Vaughan projects include the Vaughan Metropolitan Centre Black Creek and Edgeley Pond  - details on the project are here: link

The Toronto project involves the Midtown Toronto Relief Storm Sewer that is part of the city's long term and comprehensive Basement Flooding Protection program. The project will help reduce flooding for almost 900 homes during a 100-year flood event. See details on the overall program here: link

The Regional Municipality of York project involves the twinning of a wastewater collection system forcemain (pressurized flow). This has been called a a significant component of the Upper York Sewage Solutions project. See project details here: link


Canada helps protect communities across the Greater Toronto Area from flooding
and storms

Four new projects approved in four communities in the City of Toronto and the Regional Municipality of York

Climate change is happening and it is affecting Canadian communities from coast-to-coast-to-coast. More and more Canadians realize that natural hazards like floods, wildland fires and winter storms are increasing in frequency and intensity. For many communities, these hazards are significantly affecting critical infrastructure and can result in health and safety risks, interruptions in essential community services and increasingly high costs for recovery and replacement.

The Government of Canada’s Disaster Mitigation and Adaptation Fund (DMAF) is a 10-year, $2 billion national program designed to help communities better withstand current and future risks of natural hazards.

The following four projects in the Greater Toronto Area have been approved for federal funding totaling $150,388,299 and for municipal funding totaling $252,682,449.

Project Name
Federal Funding
Municipal Funding
Toronto, City of
Construction of the Midtown Toronto Relief Storm Sewer for Basement Flooding Protection


York, Regional Municipality of
York Durham Sewage System Forcemain Twinning Project


Markham, Corporation of the City of
City of Markham’s Flood Control Project
(Don Mills Channel, West Thornhill, Thornhill Community Centre)


Vaughan, City of
Implementing Vaughan Stormwater Flood Mitigation projects



An announcement was made regarding DMAF funding in Edmonton ($53,000,000) for the construction of two dry ponds in Parkallen’s Ellingson Park =-these are two of 13 planned facilities and are expected to reduce the amount of water pooling in the area by about 84 per cent: ink

An announcement was made regarding DMAF funding in Canmore, Alberta ($13,760,000) for a project involves reinforcing flood mitigation structures along several steep mountain creeks in the Bow Valley to reduce the risks of debris flooding, and re-vegetation and bio-engineering work to control erosion problems: link - more on the project here

An announcement was made regarding DMAF funding of the Calgary Springbank Off-stream Reservoir Project ($168.5 million) in Rocky View County which will divert extreme flood flows from the Elbow River to a storage reservoir to be contained temporarily until the flood peak has passed : link . The reservoir would have capacity of over 70 million cubic litres and would be located 15 kilometres west of Calgary between Highway 8 and the Trans-Canada Highway, and east of Highway 22.

More on the Disaster Mitigation and Adaptation Fund and projects:


Background on return on investment (ROI) cost benefit analysis to support the Markham DMAF application is here considering its city-wide Flood Control Program that shows a ROI, or benefit cost ratio of over 5 if total losses are mitigated - a lower ROI would result from deferral of only insured losses:

The Markham DMAF project ROI values are based on individual project costs and benefits, with these benefits based on deferred total losses (i.e., higher than insured losses). The average ROI benefit-cost ratio is 4.7 for the three Markham projects.


Benefit cost analysis for infrastructure adaptation to extreme weather and climate change using grey and green infrastructure strategies is presented in an upcoming WEAO paper provided in an earlier post: link

IDF Updates for Southern Ontario Show Continuing Decrease in Extreme Rainfall Intensities Since 1990 - Environment and Climate Change Canada's Engineering Climate Datasets Version 3.0

The Annual Maximum Series (AMS) charts in a recent post show updated trends in observed maximum rainfall volumes over various durations. Design rainfall intensities, equivalent to volumes over the various durations, are derived by fitting a statistical distribution to the observations, resulting in intensity-duration -frequency (IDF) values presented in tables and charts for each climate station. A previous post examined trends in IDF values for long-term record stations in southern Ontario based on 1990 to version 2.3 values (updated to 2001 to 2013 data) - see link - the overall decrease in intensities was 0.2 percent with more frequent, small return period, values decreasing the most.

The extended, updated version of Environment and Climate Change Canada's Engineering Climate Datasets has IDF values based on data up to 2017 and was released in March 2019. Information is available from the Environment and Climate Change Canada's ftp site through this link on their website.

Again we can compare design intensity values from 1990 with the current, updated values and determine if older design standard values are appropriate and conservatively above today's values or if updates to standards are required to reflect more intense rainfall rates. For this review, 8 of the 21 stations have had updates to IDF values since the version 2.3 datasets. The average length of record increased from 42 to over 46 years, averaged across all stations and statistics. The charts below show the average change in intensity for all durations grouped together (top chart Figure 1) and considering variations across durations (bottom chart Figure 2).

Figure 1 - Average Change in Southern Ontario IDF Values for Engineering Design by Return Period - Record-Length Weighted Changes Between 1990 and Version 3.0 Datasets for 21 Climate Stations with Long Term Records

Figure 2 - Average Change in Southern Ontario IDF Values for Engineering Design by Duration and Return Period - Record-Length Weighted Changes Between 1990 and Version 3.0 Datasets for 21 Climate Stations with Long Term Records
 Observations are that:

     Rainfall intensities are decreasing even further than in the last review.
     The changes in IDF values based on more recent observations are very small and reflect only minor random ups and downs - changes in IDF values due to assumed statistical distribution selection are greater than observed rain data changes. No “new normal” or “wild weather” due to a changing climate.
     Frequent storm intensities (those used for most storm sewer design) are decreasing for all durations.
     The more frequent the storm the greater the decrease in design intensity.
     Rainfall intensities are decreasing more for short durations than longer ones (see short duration red and orange bars in Figure 2).
     Less frequent, severe storm intensities (25 year to 100 year return periods) are deceasing on average.
     Severe storm intensities are decreasing most for short durations.

The following tables summarize values in the above charts. Note that the chart data is weighted by record length so that longer trends are given proportionately more weight. The tables show both weighted and unweighted values -giving more weight to longer record stations results in a greater overall decrease in IDF rainfall intensity statistics.

Table 1 - Trend in Southern Ontario Intensity Duration Frequency Values for 21 Long-Term Climate Stations, Weighted by Record Length - 0.4 Percent Average Decrease in Intensities 
Table 2 - Trend in Southern Ontario Intensity Duration Frequency Values for 21 Long-Term Climate Stations, Not-weighted by Record Length - 0.2 Percent Average Decrease in Intensities
What does this mean for engineering design? In general, older design IDF values or curves are conservative reflecting older, higher observed rainfall intensities. Infrastructure designed to older standards will be slightly more resilient today, having a marginally greater safety factor and higher performance under today's extreme weather conditions. Older infrastructure may be stressed by hydrologic or hydraulic factors, or intrinsically lower design standards - see previous posts here on hydrologic factors including at many southern Ontario cities in this post. How the updated values affect municipal engineering design is shown below on an annotated Table 1.

Table 1 Annotated - What has changed? What are IDF values used for? What does this mean for municipal infrastructure engineering design and resilience of sewer and pond designs?
The implications for municipal infrastructure design based on governing durations and frequencies are annotated around the first table. This shows that:
     storm sewers, designed to convey high frequency, short duration intensities, are facing lower rainfall intensities since 1990;
     major drainage systems designed for low frequency longer durations (because critical conveyance segments are often lower in the system where times of concentration are longer) are facing no change in design rainfall intensity;
     storm water ponds designed to hold low frequency, high return period, long duration storms are facing no change in design rainfall volumes.

This just reflects historical trends in southern Ontario, so how about future changes under climate change that should be considered in design? After all, Bill 138’s Planning Act amendments and O.Reg.588/17 require municipalities to identify how they will accommodate climate change effects in infrastructure policies and plans.

The American Society of Civil Engineers ASCE has created a guide that can be considered and that classifies infrastructure by it's criticality, based on potential loss of life and economic impact as well as the service life of the asset to determine an approach for addressing potential future climate change effects. The guide is "Climate-Resilient Infrastructure: Adaptive Design and Risk Management". One of the principles is that given uncertainty with future climate, one may design with today's climate if the risk class is low, as long as future adaptation is feasible. The guide also promotes an approach called the Observational Method (OM), defined as follows:

"The Observational Method [in ground engineering] is a continuous, managed, integrated, process of design, construction control, monitoring and review that enables previously defined modifications to be incorporated during or after construction as appropriate.All these aspects have to be demonstrably robust. The objective is to achieve greater overall economy without compromising safety."

The OM approach has been adapted by ASCE to designing climate resilient infrastructure and has the following steps:

1. Design is based on the most-probable weather or climate condition(s), not the most unfavorable and the most-credible unfavorable deviations from the most-probable conditions are identified.

2. Actions or design modifications are determined in advance for every foreseeable unfavorable weather or climate deviation from the most-probable ones.

3. The project performance is observed over time using preselected variables and the project response to observed changes is assessed.

4. Design and construction modifications (previously identified) can be implemented in response to observed changes to account for changes in risk.

For new subdivisions, adaptation/modifications noted in the last steps could be implemented in the future if rainfall intensities increase. Some relatively minor local system modifications representing adaptation activities could include:

     adding or modifying storm inlets with control devices to limit capture into the storm sewer (upstream of where future HGL risks are predicted);
     adding plugs to sanitary manhole covers to limit inflows (where significant overland flow spread and depth is predicted);
     modifying the outlet of stormwater ponds to optimize storage for larger storms (e.g., add intermediate-stage relief components to limit over control);
     increasing the capacity of overflow spillways in stormwater ponds to convey larger storms that cannot be stored (e.g., widen or line with erosion protection to a higher stage);
     increase pond storage capacity through grading of side slopes (e.g., steeper slopes or steps/walls) at time of sediment removal/cleaning (NB - slope material may be used to bulk up high moisture content sediment to accelerate cleaning schedule);
     sump pump disconnection of gravity drained foundation drains (weeping tiles) for lowest, at risk basements where insufficient freeboard exists to future higher HGL.

In addition, property owners in any areas of increased risk could be made aware of those and be encouraged to raise insurance coverage limits or consider lot-level flood proofing as well. The benefits of the ASCE's stated OM approach is that it can accommodate future climate change effects without over-designing or over-investing in today’s infrastructure. This is feasible if future adaptation opportunities exist in today's design and if new subdivisions have a relatively high level of resilience already (i.e., safety factors, freeboard values, redundancy, conservative design parameters) such that future changes do not drop effective performance in most areas across a system into a realm where damages will occur. There may be risks in critical sections of the infrastructure system that where designed to the limits of current standards.

Considering an OM approach for southern Ontario climate resilience we are in an observation stage (Step 3) now, having skipped Step 1 and designed most systems for historical IDF characteristics, and not having considered adaptation measures in advance (Step 2). Given that rainfall intensities have not changed, the project performance will not have changed since the system was originally designed with historical IDF values. Therefore no modifications/adaptations are required to account for rainfall trends. It is unlikely that performance variation in a new subdivision could be confidently determined for decades given that the chances of experiencing an event that tests design performance are low. Any performance monitoring may have the co-benefit of informing the baseline performance under historical design standards, as explicit consideration of safety factors is not common, and it is possible that modern systems are exceeding their intended capacity and performance level due to these intrinsic design safety factors. 

For retrofitting older infrastructure systems, the IDF data is not as critical in determining risk as is the selection of a design hyetograph that will use this data. Most older systems have level of service gaps for yesterday’s and today's climate and extreme weather, leading to current flood risks.

Looking at the OM approach for retrofitted systems, the noted changes in southern Ontario IDF values since 1990 will have no bearing on performance and flood risks and would not trigger project modifications/adaptation. Some conservative design hyetographs used in retrofit analysis do incorporate a safety factor that could account for future climate effects as well as other hydrologic (e.g. antecedent conditions) or operational uncertainties (e.g. local blockages, clogged grates). For example, some municipalities use a Chicago storm distribution that is conservative in terms of system response - this was examined in detail in this WEAO 2018 Conference Paper and presentation. That type of conservative design hyetograph pattern could limit the project response to future IDF changes experienced under less extreme real storm patterns.

What is more uncertain perhaps, at that requires observations, is the baseline performance of the retrofitted system and how well it mitigates flood risk given the diverse range of failure mechanisms possible. That is, infrastructure upgrades on the public collection system will not alleviate lot-level risks that remain, resulting in baseline performance gaps regardless of changes in IDF values or baseline system design. This should be an area of future research, i.e., to quantify baseline mitigation effectiveness (i.e., performance) - as many factors affect performance and occur together at the same time, it may be difficult to separate out what performance variations are due to weather variations versus other factors. For example, real storms have a significant spatial and temporal variability compared to simplified design assumptions (typically spatially and temporally uniform rainfall) - this was explored at a recent National Research Council workshop on urban flooding (see slides 17-19 for a recent example of real-world temporal and spatial variability compared to design assumptions).  Nonetheless, an observed gap in performance regardless of the cause can trigger adaptation/modifications to restore performance of a project to its intended level of service. This would likely be possible only if performance is significantly below expectations.


Other related posts and links:
  1. CBC Ombudsman's scathing ruling on journalistic standard violation regarding extreme rainfall reporting - link,
  2. CBC Radio Canada interview on the importance of data and gaps in media reporting - link,
  3. Financial Post OpEd on insurance industry claims correlating flood losses to extreme weather trends - link,
  4. Water Environment Association of Ontario (WEAO) Influents magazine article on flood risk drivers - link,
  5. National Research Council national workshop presentation on extreme rainfall trends (this inspired the southern Ontario IDF review in this and earlier posts) - link,
  6. WEAO OWWA joint climate change committee presentation on flood risk factors including IDF trends and hydrologic factors - link,
  7. Review of “Telling the Weather Story” report citing theoretical IDF shifts as real Environment and Climate Change Canada data - link,
  8. “Thinking Fast and Slow on Floods and Flow” exploring heuristic biases in framing and solving problems surrounding extreme rainfall and flood risks - link.

Environment and Climate Change Canada Updates Annual Maximum Rainfall Trends and IDF Statistics in Engineering Climate Datasets - Decreasing Extreme Rainfall Trends Continue in GTA

Environment and Climate Change Canada has posted updates to Annual Maximum Rainfall Trends / Series and derived Intensity Duration Frequency curve data on their website - see link. This is version 3.0 of the Engineering Climate Datasets and indicate trends in extreme rain intensities over various durations that are considered in engineering design such as municipal infrastructure design or building design. Many climate stations have had their records extended to as recently as 2017 however some maintain only the previous records in version 2.3. The following is a summary of some the updates looking at trends in storm severity based on recorded data.

Greater Toronto Area (GTA) maximum yearly rainfall trends are shown in the following charts for Toronto City (downtown 'Bloor Street' gauge), Pearson Airport (Mississauga) and Buttonville Airport (Markham):


A review of Pearson Airport climate station extreme rainfall trends considering raw data was provided in a recent National Post Op Ed - see link. Other raw data for the GTA was analyzed in a previous post.

The long term series for Toronto and Mississauga show trends that are flat (no change) or decreasing - for Toronto, the 12 hour rainfall amounts are decreasing significantly. The Buttonville Airport data has not been extended by Environment Canada in the version 3.0 datasets however the City of Markham has done so with raw data and identified decreases in short duration intensities (see IDF discussion at end of this post).

In other Southern Ontario regions trends are generally not statistically significant and can be up or down (the only possibilities really). Here are trends for Ottawa, Kingston, Hamilton and London:

The Ottawa trend are downward for short duration affecting flash flooding in urban areas. For long durations the trends are mixed - the Ottawa CDA RCS gauge has a high recent value for the remnants of hurricane Francis in 2004 and many low values at the turn of the century that drive the 24 hour rainfall trend up at that gauge - nonetheless, trends for durations of 2 hours and less that reflect convective thunderstorms are decreasing at that gauge. At the Ottawa Airport, decreasing trends are
strong and are statistically significant for durations of 10 minutes, 15 minutes and 1 hour.

Kingston has a long term record of almost 100 years. While records are not extended since the version 2.3 dataset, the trends are basically flat over the period of record as shown below:

Hamilton Airport has a moderate length record and show decreasing annual maximum rainfall amounts wince the early 1970's (see below). The longer record Botanical Garden gauge show no overall trends going back to the 1960's.

The London Ontario period of record goes back to the 1940's. Trends in annual maximum rainfall are up, flat, or down depending on the duration as shown below in the extended series: 

 In Windsor, the record has not been extended to cover recent extreme events in 2016 and 2017 (version 3.0 is the same as version 2.3). The available series show decreasing annual maximum rainfall going back to the 1940's and statistically significant decreasing trends for many durations including 10 minutes, 2 hours, 6 hours and 12 hours. It is likely those trends will 'level out' when the 2015 and 2016 storm are included.

The University of Windsor series in shown below to illustrate that short record are unreliable to make observations on overall trends - increasing trends through the 1970's in some of the charts below do not reflect overall decreasing trends over many decades as shown in the charts above.
Other records from across Canada has been undated in the version 3.0 dataset. A few are shown below. The Calgary Airport trends since the 1940's are decreasing, flat or increasing slightly - there are no significant trends in any direction for any duration.

In Edmonton, the longest record goes back a century at the Blatchford climate station. The annual maximum rainfall observed there is decreasing or flat for duration of up to 12 hours, with no significant trends.
 If we look at a shorter duration gonig back to the 1960's at the Edmonton Airport, trends are up:
 And if we look at shorter records since the 1980's like at Stoney Plain CS, the trends are down:

Take aways:

1) It is best to look at the trends over the long term and rely on the longest periods of record for estimating extreme value statistics in engineering design. An earlier review of these statistics for long term stations in Southern Ontario show small, high frequency rain intensities decreasing slightly on average and large, low frequency intensities mixed (i.e., only small increases and decreases that are insignificant in hydrologic analysis).

2) Most urban storm drainage systems are small and 'flashy' responding to short duration rainfall intensities that correspond to the 'time of concentration' of the catchment of up to a couple hours (but typically less). Trends in rainfall maximum amounts over those duration can contribute to changes in flood flows and flood losses (damages) - overall, hydrologic changes (more urbanization over decades, more intensification within earlier development) greatly overshadow any meteorologic changes. My paper in the Journal of Water Management Modeling "Thinking Fast and Slow on Floods and Flow" explores some of this as do earlier posts.

3) Small local wastewater systems may be sensitive to short duration high intensity rainfall trends as well, especially where rooftop drainage improperly or illicitly contributes inflows to those collection systems. Flow monitoring data can show a 'flashy' response in extraneous flow rates that stress system capacity and contribute to basement flooding / sewer back-up risks.

4) Large surface water drainage collection systems (channel systems and local creek tributaries), as well as wastewater collection systems may be most sensitive to longer duration rainfall intensities (cumulative volumes). For this reason, some municipalities (Ottawa, York Region) have adopted long duration design rainfall hyetographs to assess system capacity.

5) Despite the lack of overall extreme rainfall trends in the regions screened above, some other regions in Canada may have other trends. An earlier review of the version 2.3 datasets across the country showed some regions with more increasing than decreasing trends - see post here with regional summaries of trends direction and significance. See post here with a review of long term station trends (shows more increases than decreases in Maritimes and Newfoundland).

Stay tuned for a review of IDF updates with the version 2.3 datasets. Previous work in Southern Ontario municipalities using earlier data and some updated data (City of Markham's Toronto, Mississauga and Markham gauge review, for example) has not shown appreciable changes in IDF values - see previous post.

Below is an initial review of 5-minutes design rainfall intensities for return periods of 2-year to 100-years considering extended datasets:

The downtown Toronto design rainfall intensities are decreasing since the 1990 values for all return periods considering extreme rainfall observations data up to 2017.

The Mississauga design rainfall intensities (at Pearson Airport) are decreasing since the 1990 values for all return periods considering extreme rainfall observations data up to 2017.

The Markham design intensities (at Buttonville Airport) are decreasing since the 2003 values for all return periods considering extreme rainfall observations data up to 2016 (raw data from Environment Canada and analysis by City of Markham for 2016 values).

AN ECONOMIC ANALYSIS OF GREEN V. GREY INFRASTRUCTURE - Robert J. Muir, M.A.Sc., P.Eng., Fabian Papa, M.A.Sc., M.B.A., P.Eng.

The following paper was presented at the WEAO 2019 Annual Conference in Toronto, Ontario. A pdf version is available here. The slide presentation is included at the bottom of this post.
A note to TRIECA 2019 attendees where these results were highlighted: the Strategies A, B and C in the TRIECA presentation correspond to Strategies A, C, and D below:


Robert J. Muir, M.A.Sc., P.Eng., Fabian Papa, M.A.Sc., M.B.A., P.Eng.


     There is much healthy debate in the industry relating to the implementation of green infrastructure solutions for managing stormwater runoff and which is not uncommon when there are changes to traditionally employed methods. A rational approach to assist in the planning for the type of storm drainage infrastructure – that is, green or grey in the context of this paper – that might be appropriate to implement should incorporate measurements (or reasonably reliable estimates) of both performance (benefits) and costs over an appropriate time horizon.

     This paper examines, at a high level, the benefits derived from both green and grey infrastructure relative to their associated costs to identify the economic return on investment as measured by benefit-cost ratios. The analysis uses actual cost information (including capital as well as ongoing maintenance costs) derived from projects in both Canada and the US. Benefits considered include avoided damages (both insured losses and total losses) and, particularly for the case of green infrastructure, the additional benefits of reduced erosion mitigation and estimates of willingness to pay for water quality improvements. Further, the analysis considers a relatively large (City-level) scale, using the City of Markham as a case study and, as such, provides an example of the information that can be useful for establishing infrastructure strategies at that level. Although not explicitly considered in this work, the philosophy (approach) and methodology remain valid for other levels of analysis (e.g., Secondary Plans, individual municipal or private sector development projects, etc.) as well as higher level policy evaluation.

     The following sections present i) a methodology for benefit-cost analysis of infrastructure strategies, including a history of such analysis and a review of current practice, and ii) the results of an analysis applying this methodology across the City of Markham.  The analysis considers flood control benefits derived from reported losses and other watershed benefits for various strategies including all-grey, all-green and blended servicing approaches. Conclusions, including considerations for setting public policy and funding priorities for infrastructure investments are provided.


History of Benefit-Cost Analysis in Water Resources

     There is a long history in benefit-cost analysis for water resources projects in North America and around the world.  Kneese (2000) describes the evolution in the United States dating back to the beginning of the 20th century when the Federal Reclamation Act of 1902 required economic analysis of projects, and 1936 when the Flood Control Act established a welfare economics feasibility test that benefits “to whomsoever they may accrue” must exceed costs. Boz and Zwaneveld (2017) review a century of benefit-cost analysis applied in the Netherlands, including in 1901 for the enclosure of the Zuiderzee on the North Sea. In Canada, the Royal Commission on Flood Cost Benefit for the Red River Floodway was completed in 1958.

     In Hydrology of Floods in Canada, Watt (1989) describes economic efficiency criteria and principles associated with river flood risk reduction projects. He notes “It is therefore reasonable to require that all projects that provide or improve flood protection be justified economically before public funds are allocated.” Watt adds that “contrary to public opinion, the direct and indirect benefits of flood control tend to overshadow the intangible benefits” and therefore “expected benefits should exceed cost by a sufficient margin and the level of protection should not be pushed beyond the point where the additional costs exceed the incremental benefit.” As flood control projects rank high in terms of public welfare, these are often approved even when the benefit-cost ratio is only marginally higher than unity and occasionally when it is less than unity.

     The principle of cost-effective infrastructure investment is embedded within the Ontario’s Provincial Policy Statement (Ontario Ministry of Municipal Affairs and Housing, 2014), which indicates at a high level that “Infrastructure … shall be provided in a coordinated, efficient and cost-effective manner.” It is reinforced in new regulations which requires that “[for] each asset category, the lifecycle activities that would need to be undertaken to maintain the current levels of service” must be determined in municipal asset management plans (Ontario Ministry of Economic Development, Employment, and Infrastructure, 2017). Furthermore, these activities must consider “the lowest cost to maintain the current levels of service.”

     An evaluation of project costs is required as part of local studies involving flood control, such as through Ontario Municipal Class Environmental Assessments (Municipal Engineers Association, 2015). Despite this, formal benefit-cost analysis is uncommon in practice, often as projects are implemented to meet specific performance standards, or are selected based on comparative alternative costs, as opposed to any overall cost-efficiency goal. The City of Stratford Storm System Master Plan (Dillon Consulting Limited, 2004) demonstrated that benefit-cost ratios could be developed on a sewershed scale to assess the feasibility of infrastructure improvements, and to guide and prioritize further studies for flood damage reduction project implementation.  Benefit-cost analysis may be completed for large-scale flood control projects where significant costs for strategically critical regional projects attract public scrutiny. For example, the Springbank flood storage project to reduce City of Calgary river flood damages was recently subject to such analysis (IBI Group, 2015). 

     Numerous challenges impede benefit-cost analysis for smaller, local flood control projects. These include i) lack of regulatory requirement, ii) previously limited availability of flood damage data (insured and uninsured losses), iii) previously limited availability of lifecycle costs, especially for emerging green infrastructure measures, iv) the fragmented nature of small-scale, distributed projects that challenge system-wide performance/benefit assessment, and v) the sometimes fragmented jurisdiction for large systems across multiple municipalities.  Eckstein (1958), in foundational work on water resources development economics, noted that system-wide assessments are necessary for entire programs, such as for river basins, and cited the US Army Corps of Engineers’ “308 surveys” that developed comprehensive plans for improving river navigation, power development, flood control and irrigation nearly a century ago. He suggests that “project benefit-cost ratios are meaningless and misleading, unless they represent the incremental benefits and costs of projects in a specified plan of development.”

Current Approaches to Benefit-Cost Analysis

     The Treasury Board of Canada Secretariat (2007) has developed a guide for benefit-cost analysis of regulatory proposals in Canada. The guide indicates that “all regulatory departments and agencies are expected to show that the recommended option maximizes the net economic, environmental, and social benefits to Canadians, business, and government over time.”  Since regulations surrounding water resources within a province's boundaries fall within the constitutional authority of that province, federal guidelines may not apply to most local water resources projects. This would include most local, municipal infrastructure projects.

     The Disaster Mitigation Adaptation Fund (DMAF) is a new fund to invest in the public infrastructure needed to mitigate impacts of climate change and strengthen resilience to natural hazards and extreme weather events (Infrastructure Canada, 2018).  The fund targets moderate to large projects with a minimum cost of $20 M and requires an assessment of return on investment, defined as the ratio of total benefits over the project service life to lifecycle costs. Eligible projects must achieve a ratio of 2:1 or greater. Benefits represent averted damages and may include any quantifiable socio-economic and environmental damages.  No guidance is provided on the economic damages that shall be considered, whether direct or indirect.

     National Resources Canada (NRCan) and Public Safety Canada (PSC) (2017) released draft guidelines on flood vulnerability functions focused on defining riverine flood damages. The guidelines suggest three approaches to estimating tangible damages as follows:

“1. The first entails an examination of the floodplain immediately after the water recedes. If such estimates were available for every flood over a period of many years, a damage-frequency curve could be created;
2.    An alternative method is to determine the damage caused by three or four recent floods whose hydrologic frequency can be determined and a smooth damage frequency curve plotted through these points; however, for most floodplains, changes in land use with calendar time prevent direct usage of a damage-frequency relationship from historical damages; and
3.    The third method entails hydrologically determining various flood elevations for specific flood frequencies and deducing synthetically the damages that would occur given these flood events. This analysis provides a synthetic damage-frequency curve from which one can estimate average annual damages for a given study area.”

     NRCan and PSC commented that the third method is the “best approach for obtaining accurate and representative estimates of damages based on current economic factors,” citing changing land use conditions as a limitation for relying on historical damages, and “large voids in the data” and insufficient events to rely on the first two methods.  While the third method may be ideal in terms of accuracy, particularly at a local project scale, at a planning level where flood mitigation strategies are developed and funding requirements for asset management and capital improvement plans are set, sufficient analysis is generally unavailable to support it.  The third method may be described as a ‘bottom-up’ property-scale approach where the exposure of individual properties impacted by a project is assessed.  In contrast, the first and second method represents ‘top-down’ approaches where aggregated data may be applied over larger planning areas and jurisdictions.

     Recently, researchers at the University of Waterloo’s Intact Centre on Climate Adaptation, the Insurance Bureau of Canada (IBC) and the International Institute for Sustainable Development  presented case studies with comparative costs and benefit-cost analyses for ‘natural infrastructure’ including engineered green infrastructure on-site controls, and natural heritage features including wetlands and naturally occurring ponds (Moudrak et al., 2018).  While the report concludes the “Natural infrastructure can be a cost-effective way to mitigate material financial losses that would otherwise result from flooding,” the case studies have many limitations and i) omit benefits of grey infrastructure alternatives, precluding complete assessments of benefits and costs of all potentially practical and/or feasible alternatives, ii) substitute one-time capital cost differences as annual operational services, overestimating expected benefits, iii) replace published local flood damage benefits with ‘meta-analysis’ (i.e., global literature search data), increasing expected benefits, iv) present atypical watershed settings (e.g., with extensive wetland coverage upstream of a flooding Special Policy Area) as broad, practically-encountered typical conditions, v) do not factor averted damages during rare events by their probability, conflating high event benefits with actual, lower annual benefits, and vi) apply generic US river flood damage indices to a local, master-planned subwatershed with no actual riverine flood risks, misrepresenting benefits in an Ontario setting with advanced floodplain management policies. These research case studies, while widely promoted in the media, do not follow any of the NRCan and PSC methods for damage assessment nor offer reliable benefit-cost analysis considering local data or settings.

Grey and Green Infrastructure Strategies
For Flood Control and Watershed Restoration

     This paper demonstrates the application of the NRCan and PSC’s second method for flood damage assessment, relying on the growing set of damage datasets in Canada. It focuses on urban flooding and basement back-up related to infrastructure system performance, as opposed to riverine flooding, where property-scale damage estimates are not readily calculated. This ‘top-down’ region- to neighbourhood-scale approach can support the development of municipal infrastructure strategies and the overall evaluation of distributed mitigation measures, including green infrastructure.  The incorporation of reported flood damage data is intended to improve the accuracy of assessments that have sometimes relied upon limited local modelling or data (i.e., ‘meta-analysis’ and generic damage indices from other jurisdictions).  As green infrastructure is accepted to contribute to watershed restoration benefits such as water quality improvements and water balance/erosion mitigation, these potential benefits are also assessed for a range of infrastructure strategies in the City of Markham.

     Strategies evaluated are described below and include all-grey, all-green and blended strategies that consider both city-wide, and more focused local implementation:

i) Strategy A represents Markham’s existing Flood Control Program activities, predominantly consisting of grey infrastructure storm and sanitary sewer conveyance system capacity upgrades. Best practices and programs for private-side extraneous flow reduction and plumbing protection are included as well as isolated, centralized green/natural infrastructure (i.e., centralized wetland). Water quality retrofits (e.g., oil and grit separation) are included and may represent up to 10% of capital costs.

ii) Strategy B represents city-wide implementation of green infrastructure to achieve watershed benefits (i.e., water quality, water balance and erosion control) and some degree of expected flood control.  Costs are based on design volumes for small storms (i.e., not flood control).

iii) Strategy C represents focused implementation of green infrastructure in older service areas (i.e., 25% of the city representing pre-1980 service areas) to achieve local flood reduction benefits and some watershed benefits.  Costs are based on higher volumes than those adopted for CSO control.

iv) Strategy D represents implementation of grey infrastructure in 90% of pre-1980 service areas and green infrastructure in 10% to achieve flood control benefits. Watershed benefits will be partially realized.

     Grey infrastructure, including storm and wastewater conveyance and storage upgrades have served as the traditional engineered approach to providing urban flood damage mitigation and is recommended in most Municipal Class Environmental Assessment studies.  Green infrastructure has been proposed recently as an urban flood mitigation measure by some academics, landscaping professionals and environmental agencies, including many with long-standing interests in promoting urban revitalization, innovative adaptive management measures and watershed environmental restoration. Organizations representing Ontario professional engineers (Ontario Society of Professional Engineers, OSPE), the wastewater and stormwater industry (Water Environment Association of Ontario, WEAO), and many Ontario municipalities (Ottawa, Barrie, Markham, and Guelph to name a few) have commented that green infrastructure, low impact development stormwater management best management practices (LID SWM BMPs), may worsen flood risks in some urban areas by stressing flood prone wastewater systems and property foundations (Muir, 2018d).

Assessment of Regional and Local Flood Damages 

     The Insurance Bureau of Canada (IBC) has compiled insured loss and loss adjustment expense data for across Canada and in Ontario. This includes total losses from all perils including fire, hail, etc. and ‘water damage’ losses considering events classified as flood, water, storm or hurricane perils.  The data sources include detailed CatIQ data for the recent 2008 to 2017 period and various surveys by IBC for earlier periods.  A review of raw data was completed by City of Markham and included the reclassification of some peril losses; for example, the 19 August 2005 flood event was reassigned to the Ontario ‘water damage’ dataset.  Ontario water damage losses are illustrated in Figure 1.  Across Canada, the percentage of losses resulting from water damage has been noted to be decreasing slightly, declining from 34.0% of losses prior to 2008, to 31.7% after 2008 (Muir, 2018c).

     The US Army Corps of Engineers (US ACE, 1989) illustrates the analysis approach to determining “expected annual damage” or EAD. The IBC’s Ontario water damage data is used to develop a probability distribution of annual losses that can be used to calculate the EAD.

FIGURE 1. Ontario Catastrophic Losses - Water Damage (Flood, Storm, Hurricane, Water perils)

Cumulative Damages Prevented by Flood Mitigation Efforts (Benefits)

     Cumulative damages prevented over a project’s service life, representing benefits, may be based on EAD using insured loss and loss expenses but must also recognize that total uninsured damages are higher, and that averted damages are less than the total damages.  Swiss Re (2016) notes that while insured losses include tangible direct damages such as loss of internal and external contents and structural repairs and cleaning, indirect damages that may not be insured include tangible indirect costs such as financial losses, opportunity costs and other clean-up costs. A ratio of total to insured losses of 1.5 is cited for one extreme flood event in Toronto in July 2013. Meanwhile an analysis of data from Munich Re’s NatCatSERVICE based on a wider range of hydrological events in Canada from 1980 to 2017 (Munich Re, 2018) results in a loss-weighted total to insured loss ratio of 1.8.  Averted damages are less than total damages considering that i) the design level of service for municipal flood mitigation projects may be less than the return period of events driving flood losses,  ii) private property drainage and plumbing limitations can contribute to flood damages even after public infrastructure is upgraded (e.g., Toronto Water (2016) notes "High groundwater and private side drainage issues a contributing flooding factor"), iii) private property plumbing protection measures such as backwater valves and sump pumps may fail to operate due to inadequate maintenance or power interruption, and iv) lower risk areas may not warrant public infrastructure upgrades based on limited cost-effectiveness and may continue to have outstanding risks in the future (Toronto Water, 2018).

     For the purpose of the analysis presented in this paper, it is assumed that higher damages and potential benefits due to total losses above insured losses, and limitations to averting damages below that total would negate each other. Therefore, benefits representing averted damages, a fraction of the total damages, are assumed to equal to insured loss and loss expenses.  While this approach results in some uncertainty in terms of absolute benefits and benefit-cost ratios, it does support the comparative evaluation of benefits of alternative flood control technologies.

     Flood mitigation measures may operate over service lives of 25, 50 or 100 years, depending on the nature of the measure. Typically, a service life of 100 years can be assumed for modern concrete pipe infrastructure (e.g., large storm sewers) or plastic pipe infrastructure (e.g., plastic wastewater sewers or plastic lined concrete wastewater sewers or plastic underground storage devices such as arched modular tanks). Ottawa’s State of the Asset Report indicates an expected service life of roughly 100 years for concrete wastewater pipes (City of Ottawa, 2017) and Markham’s Asset Management Plan adopted a 100 year service life for concrete and PVC storm sewer pipes (City of Markham, 2016). A service life of 25 years can be assumed for green infrastructure surface features such as rain gardens that would require reconstruction/full refurbishment after 25 years – research presented Sustainable Technologies Evaluation Program (STEP) report titled Assessment of Life Cycle Costs for Low Impact Development Stormwater Management Practices indicates a life span of 25 years for bioretention measures, 30 years for permeable interlocking concrete pavement, and over 50 years for infiltration trenches and chambers (Toronto and Region Conservation Authority and University of Toronto, 2013).

     Green infrastructure operation may result in adverse impacts to infrastructure and properties due to infiltration.  Infiltration can worse sewer back-up and seepage damages, as basement flooding insurance risks in Markham have shown a strong quantitative correlation to sanitary sewer infiltration risk factors.  Infiltration may also lower soil resistivity due to the presence of chlorides and accelerate deterioration of watermains.  These adverse impacts are not quantified in the analysis but may lessen the effectiveness of green infrastructure strategies that mitigate surface flow stresses while aggravating subsurface ones.

Watershed Restoration Benefits (Water Quality and Erosion Mitigation)

     Infrastructure improvements can yield a variety of benefits beyond direct, tangible flood damage reduction.  Grey infrastructure upgrade projects that increase stormwater conveyance capacity, such as within the Markham Flood Control Program, can incorporate water quality improvement measures such as oil and grit separators to achieve other benefits. Activities that increase sanitary capacity and decrease extraneous flow stresses, such as sanitary downspout and foundation drain disconnection programs, can reduce the risk of wastewater overflows during rare, extreme events.  These secondary benefits are considered to be small in relation to primary flood control benefits and are not quantified here.

     Green infrastructure measures can improve water quality and alter the water balance, reducing runoff volumes and erosion stresses in receiving watercourses, contributing to habitat restoration or enhancement.    The willingness to pay for surface water quality improvements due to green infrastructure source controls has been estimated by two methods in an evaluation of Rouge River watershed source controls (Marbek, 2010). Values have been estimated to be $52.35 and $141.32 per person per year in 2010 and 2007 studies, which is approximately $61.37 to $175.71 in 2018 dollars, adjusting for 2% inflation a year. The average value is approximately $119 per person per year in 2018 dollars. This value may be factored by the population of Markham of 329,000 to yield a willingness to pay for surface water quality of $39.2 M per year. This estimated benefit is noted to be several times greater than the flood damage reduction benefit presented later, which warrants discussion on validity, and practicality for funding (see Conclusions).  (That is, it ought to be subject to a test of its reasonability in this context.)

     The benefit of erosion stress reduction due to lower runoff volumes may not be readily assessed given the stochastic and dynamic nature of erosion processes. Furthermore, runoff volume reductions may not be sufficient to stabilize erosion processes in watersheds that are highly urbanized or lessen restoration activities where infrastructure design and land use practices have put asset and property at risk even under natural erosion conditions (e.g., encroaching on natural meander belt widths of watercourses). The annual cost of Markham’s erosion restoration program is $1.2 M.  Assuming (perhaps overly optimistically) that half of this cost could be avoided or deferred through water balance alteration, annual benefits of $0.6 M could be achieved.

Other Triple-Bottom-Line (TBL) Benefits

     Analysis of a broad range of benefits of green infrastructure measures have been pursued recently including as part of insurance industry research noted earlier (Moudrak et al., 2018).  Benefits estimated as part of the development of municipal infrastructure strategies have included air pollution and carbon reduced by vegetation, heat island effect reduction, property value increase, recreational value increase, and economic water quality benefits, such as in The Green First Plan in Pittsburgh (Mott McDonald, 2016).  In that evaluation, all non-flood benefits represented 17% to 27% of flood control benefits with over half of those non-flood benefits being due to property value increase.  Economic water quality benefits varied from 1.5% to 3.1% of flood benefits.

Flood Risk Mitigation and Watershed Restoration Lifecycle Costs

     The lifecycle cost of grey and green infrastructure to achieve flood reduction and other benefits can be estimated using historical project capital costs and projections of system-wide program capital costs. Operation and maintenance costs may be based on ongoing program costs, expressed on a unit area basis. Total lifecycle costs must also consider the depreciation of infrastructure assets based on periodic rehabilitation/restoration and end of service life replacement.

     Capital costs for Markham’s Flood Control Program include a range of low-cost programs and best practices focused on immediate risk reduction (e.g., sanitary downspout disconnection, private plumbing protection with backwater valves/sump pumps), as well as higher-cost, long-term storm and sanitary infrastructure capacity upgrades.  The cost of programs and best practices is relatively minor and is estimated at $3 M which equates to approximately $1,300 per hectare (i.e., considering approximately 2,360 hectares of pre-1980 serviced land exhibiting higher flood risk due to historical design standard limitations such as partially-separated sewers with foundation drain connections to the sanitary sewer system, and limited dual drainage and/or major overland flow design). Sanitary system upgrades are estimated at $26 M (2016 dollars) based on the current draft Master Plan that identified upgrades for 1.5% of the sanitary collection system to meet a 100-year level of service against basement flooding, and to prevent sewer surcharging during 25-year storm events.  This amounts to approximately $11,000 per hectare. The cost of storm system upgrades is based on constructed and planned construction projects and is updated periodically to set ‘Stormwater Fee’ rates for property owners – these have been estimated at $234 M for storm system upgrades (2015 dollars) and include internal staffing costs to implement the program, as well as all external design, contract administration and construction costs, expressed in 2014 dollars. The total storm and sanitary system upgrade costs of approximately $260 M equates to 5.9% of storm and sanitary system asset values based on the city's Asset Management Plan ($2,075 M in wastewater assets, $2,335 M in storm water assets). Accounting for inflation of 2% per year, the storm capital cost is approximately $253 M in 2018 dollars, and sanitary capital costs are $27 M in 2018 dollars, resulting in a total program cost of $283 M (including $3 M for the City’s Flood Control Program, as noted earlier). This amounts to approximately $120,000 per hectare.

     Operation and maintenance costs for storm and sanitary infrastructure include periodic inspection such as CCTV inspection and a range of minor repair activities including flushing, debris and calcite removal, and local repairs of deteriorated pipe, joints and connections. The net impact on operation and maintenance activities is assumed to be nil for grey infrastructure where capacity upgrades replace existing infrastructure that already undergoes these activities. Some minor net benefits can result from sewer upgrade activities given that replaced infrastructure is consistently over 50 years old and was installed using less robust design and construction standards. Upgraded grey infrastructure is expected to have lower operation and maintenance costs for repairs (i.e., due to new higher standards for bedding, joints, connections, material, etc.) and have lower infiltration stresses for upgraded sanitary mainlines, maintenance holes and laterals, lowering pumping and treatment costs (in addition to deferring or avoiding capacity expansion costs). In some cases grey infrastructure capacity upgrades also provide other additional benefits, supporting long term growth where service capacity is limited, and addressing existing operational issues (e.g., improving longitudinal slopes to improve self-flushing and reduce debris build-up). In addition, water supply upgrades such as the replacement of cast-iron watermains may also be completed concurrently with sewer upgrades, resulting in capital cost savings of approximately 25% ($150/m), operating cost savings through leak reduction, and improved service reliability and lower emergency repair costs (i.e., fewer main breaks). These grey infrastructure benefits are not included in this analysis.

     Depreciation of grey infrastructure is assumed to occur uniformly over the service life and can be expressed as an annualized value based on a percentage of the initial capital cost. For example, assets with a 100-year service life are assumed to depreciate 1% of initial capital cost each year. This annual depreciation is $1,200/hectare/year, or $2.83 M per year over the 2,360 hectare study area.

     Green infrastructure capital costs have been estimated based on several sources including i) recently constructed projects in the City of Markham and across Ontario, representing 24 projects with an average cost of $575,000 per total hectare (Muir, 2018a), ii) 1100 projects in the City of Philadelphia’s Clean Water Pilot with budget costs of $568,000 per hectare and median construction costs of $872,000 per impervious hectare in 2015 dollars (Muir, 2018b), and iii) 127 projects in Onondaga County, New York with average construction cost excluding green roof projects of $783,000 per impervious hectare (Muir, 2018b). Adjusting for inflation, assumed to be 2% per year, a capital cost per hectare of $603,000 per hectare in 2018 dollars is used herein, considering Philadelphia’s extensive dataset. This reflects storage volumes of 1 to 2 inches (25 to 50 mm) for combined sewer overflow (CSO) control (and are used herein to estimate costs of green infrastructure to achieve watershed benefits, excluding flood control).  These costs may also be used to estimate capital costs to achieve watershed restoration benefits including water quality improvements and water balance alterations that contribute to erosion mitigation  It has been estimated that green infrastructure storage capacities could be doubled with an increase in construction costs of 14 to 27% to provide flood control benefits (Water Environment Federation, 2015). Adding 20.5% (being the average of the noted percentages) to the CSO control costs, the unit cost for providing flood control would thus be estimated at $726,000 per hectare.

     Operation and maintenance costs for green infrastructure have been estimated based on actual Philadelphia program costs considering a range of measures including bump-out, bump-out and storage trench, infiltration / storage trench, rain garden, subsurface basin, and tree trench features. The annual operation and maintenance cost is $20,000 per impervious hectare across all feature types (Muir, 2018b). The percentage impervious coverage in Markham has been measured to be 44% in 1999 and infill/expansion of up to 2017 based on orthophoto digitization suggest an overall impervious percentage of 50% (City of Markham, 2018a). The annual operation and maintenance cost is $10,000 per total hectare per year considering that imperviousness ratio.

     Depreciation of green infrastructure is also assumed to occur uniformly over the service life and can be expressed as an annualized value based on a percentage of the initial capital cost. For this analysis, assets are assumed to have a range of service life durations with one third having a 25-year, one third having a 50-year, and one third having a 100-year service life, with depreciation of 4%, 2% and 1% of initial capital cost each year, respectively.  With a blended depreciation rate of 2.33% and capital cost of $603,000 per hectare for watershed restoration, the depreciation cost is $14,100/hectare/year.  Meanwhile with a capital cost of $726,000/hectare, the depreciation cost for flood control is $17,000/hectare/year.

It is noted that the cost figures from US sources have not been adjusted to account for exchange rate differences and, as such, may somewhat underestimate costs for green infrastructure based on the prevailing currency exchange rates during the period of those studies and at the time of writing.

Benefit-Cost Ratio for Urban Flood Mitigation

     The benefit-cost ratio characterizes the economic efficiency of a flood control project or strategy.  Estimated ratios may be used to compare projects and strategies and may also be compared against other industry thresholds. Infrastructure Canada’s DMAF expects that projects will achieve a benefit-cost ratio of 2:1 (2018), while a ratio of 1.3:1 has been suggested for the investment of public funds for flood mitigation projects (Watt, 1989; Eckstein, 1958). The benefit-cost analysis approach described herein was followed as part of the City of Markham’s recent DMAF funding application to demonstrate a favourable ratio for ongoing projects within its city-wide Flood Control Program.

     The discounting of future costs and benefits is typically done to reflect the time value of money and to express both costs and benefits as cumulative present values, or a net present value, expressed in constant dollars. Watt (1989) has suggested “the appropriate interest rate is the rate at which governments and public utilities can borrow capital in the open market” and cited the Treasury Board’s recommendation to use real, as opposed to nominal rates.  Currently Infrastructure Ontario’s borrowing rates range from 2.7% to 3.6% for amortization periods of 5 to 30 years, respectively (Infrastructure Ontario, 2019).  In the case of Markham’s Flood Control Program, costs are funded through reserves such that the discount rate is an opportunity cost equivalent to the City’s investment earning rate, as opposed to a borrowing rate. The City’s third quarter investment review (2018b) cites a budget average rate of return of 2.55% and an actual return of 3.23% which is in line with Statistics Canada’s (2018) most recently published Ontario year-over-year inflation rate of 3.1%. Consequently the real rate, adjusted for inflation, is essentially nil and therefore no discounting of benefits and costs is included in this analysis.  That said, this analysis may be further expanded to more fully consider the effects of such discounting and, perhaps more interestingly, the sensitivity of its results to varying discount rates; nevertheless, it is beyond the scope of this particular work.

Benefit-Cost Ratio for Watershed Restoration 
and Indirect Triple-Bottom-Line

     The evaluation of infrastructure strategies and projects in Ontario, with only rare exceptions, does not quantitatively assess the economics of environmental benefits. That is, strategies for CSO reduction in wastewater systems are advanced to meet standards like Procedure F-5-5 for volumetric control (MECP, undated), and projects to advance surface water quality control are advanced to meet generic sizing volumes that target treatment efficiencies (MECP, 2003), but not to meet any receiving water outcomes that could be evaluated for benefits.

     The benefit-cost ratios attributed to water quality improvements and erosion mitigation, both key outcomes of green infrastructure implementation, are assessed in the analysis below.  The ratios are compared with flood damage reduction ratios to assess the relative contribution of various benefit types (i.e., flood, erosion, water quality) toward the overall strategy benefits (and to assess reasonability).


Ontario and City of Markham Expected Flood Damages and Benefits

     A Gumbel statistical distribution of Ontario water damage losses presented in Figure 1 was created using data from the year 2000 to 2017 to estimate EAD for the Ontario region. Earlier data was not used given that the losses appear to be non-stationary (i.e., losses are increasing, and the exclusion of this data will result in higher benefit values). From this distribution, the 2-year losses are $146 M while the 100-year losses are $1.16 B, reflecting the wide range in annual damages for typical and rare conditions.  Integrating across all probabilities, the EAD (insured losses and loss adjustments) for the recent period is $292 M in Ontario, which represents 46% of Canada-wide water damage losses.

     The local EAD estimate for the City of Markham has been scaled based on population. That is, Markham losses are 2.45% of Ontario losses based on a Markham/Ontario population ratio of 329,000 / 13,448,000. Population is considered to be a suitable scaling factor for scaling economic data given recent analysis by the Conference Board of Canada for York Region. Using elaborate analysis, the Board determined that the Markham GDP was $19.3 B in 2018, compared to an Ontario GDP of $825.8 B - the Markham/Ontario GDP ratio was found to be 2.33%, which is quite similar to the population ratio, indicating that it is a suitable scaling factor (Markham, 2019). The Markham insured EAD is therefore estimated to be $7.13 M, or 2.45% of Ontario insured losses, based on the population ratio. In municipalities characterized by extensive newer, lower-risk development, or extensive older, higher-risk development, scaling of EAD may be based on areas or other factors.

     As noted in the Methodology section, EAD derived from insured losses is assumed to represent benefits of averted damages, recognizing that total losses exceed insured losses and that municipal infrastructure works and property protection measures only partially avert potential damages.

Lifecycle Costs for Flood Mitigation and Watershed Restoration

     The lifecycle costs for grey and green infrastructure strategies in Markham are summarized in Table 1. 

Strategy - Infrastructure Type
Area Controlled
Capital Depreci-ation ($/ha/yr)
Net O&M

A – Grey (Storm/Sanitary Upgrades)
2360 ha (25%)
B – Green (25-50 mm Volume City-wide)
9450 ha (100%)
C – Green (> 50 mm Volume, Pre-1980 Areas)
2360 ha (25%)
D – Grey 90% / Green 10% (Pre-1980 Areas)
2124 ha
236 ha
2360 ha (25%)

Benefit-Cost Ratio of Grey and Green Infrastructure Strategies for Flood Mitigation and Watershed Restoration

     Table 2 summarizes annual lifecycle costs and annual benefits for i) flood damage reduction, ii) estimated willingness to pay for water quality improvements, and iii) potential erosion restoration reduction benefits for various infrastructure scenarios.  The ratio of benefits and costs for each benefit type as well as total benefit-cost ratio is shown.

1 Flood damage reduction benefits estimated at 50% of EAD.
2 Water quality and erosion benefits estimated at 25% of city-wide benefits.
3 Water quality and erosion benefits estimated at 2.5% of city-wide benefits.

     A top-down approach to assessing flood damages based on the statistical analysis of reported losses is an efficient means of estimating the benefits associated with avoided (or averted) damages resulting from infrastructure strategies.  Losses reported at a regional scale, like Ontario, may be readily scaled to assess losses and benefits related to urban flooding on a city-wide scale.  While not illustrated here, such losses have be scaled further to assess benefits at an individual project level within Markham’s overall Flood Control Program. Averted damage benefits due to infrastructure investments are not readily available but have been estimated to be equivalent to reported loss and loss adjustment expenses, which is a fraction of total insured and uninsured damages.  These benefits may be assessed without individual property-scale evaluations (e.g., using depth-damage curves and local vulnerability assessments) that are typically only available for detailed infrastructure project assessments.  While benefits considered here may be increased to account for other averted indirect damages (e.g., lost work, etc.) or broader social and environmental benefits, these are considered to be minor in relation to direct flood damages (Watt, 1989; Mott McDonald, 2016).

     The results of this analysis suggest that there can be an extremely large gap in economic performance between green and grey infrastructure solutions, with the latter providing returns on investment that can be up to two orders of magnitude higher than the former. A grey infrastructure approach (Strategy A) appears to satisfy the industry thresholds for economic efficiency with over 2 dollars of direct benefits for each infrastructure dollar invested.  However, the benefit-cost ratio estimates for green infrastructure approaches (e.g., Strategies B and C) appear to be significantly below thresholds, such that costs exceed benefits, even when sizeable intangible benefits for water quality improvement, are assigned.  While the green infrastructure benefit-cost performance improves under a focused implementation with higher capacity works in pre-1980 areas to maximize flood control benefits, costs still exceed benefits by almost 4:1, omitting infiltration impacts which could lower net benefits. This unfavourable economic efficiency for focused green infrastructure implementation is achieved even with a very generous willingness to pay value for water quality improvements – those benefits exceed flood damage reduction benefits and may not practically receive public acceptance when seeking funding, considering overall municipal tax or fee impacts. A blended approach (Strategy D) that combines grey and very localized green infrastructure across only 2.5% of the city (10% of pre-1980’s) improves the economic efficiency such that the benefit-cost ratio approaches unity, albeit at a three times higher cost and a third of the efficiency of a 100% grey approach (Strategy A).

     This particular analysis which, to be clear, is an early step in the development of a more comprehensive method of assessing project benefits and costs, and it is certainly not intended to provide a universal, generalized solution.  Its results suggest that appropriately comprehensive economic analyses are warranted to help analysts and decision makers assess infrastructure investment options. Moreover, the development of broad-reaching water management policies (e.g., at the provincial level) on how to implement green infrastructure solutions, or on how to prioritize funding (e.g., at a federal level), cannot be sensibly conducted in the absence of such considerations. Finally, it is suggested that the development of guidance documents to support the assessment of green and grey infrastructure options from both the technical and economic perspectives, as now being pursued by National Research Council Canada (NRC), would be a valuable addition to industry practices to help harmonize the industry’s perception and understanding of these matters as well as the application of such assessments.  Additional effort is needed to: (i) appropriately enumerate all the potential benefits and costs (whether they be categorized as direct or indirect, tangible or intangible) associated with alternative infrastructure solutions (whether they be categorized as green or grey, or simply infrastructure options); and (ii) to sensibly quantify the value of those indirect and intangible benefits and costs such that they are appropriately representative and meet tests of reasonability relative to other, directly and tangible, benefits and costs.  To the extent possible, rhetoric should not form the basis of value estimation, but rather should be replaced with reasonable estimations and, to this end, uncertainty analysis may assist in forming an integral part of a fully comprehensive assessment of benefits and costs.


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